1. Field of the Invention
The present invention relates to signal processing and more specifically to signal processing by analog multiplication.
2. Description of the Prior Art
In the present state of the signal processing art, analog multiplication may be accomplished by utilizing such techniques as quarter-square multiplication, triangular averaging multiplication, pulse width/pulse height multiplication, and variable transconductance multiplication. Quarter-square multiplication is based upon the algebraic identity xy=1/4[(x+y).sup.2 -(x-y).sup.2 ]. Diode networks are used to perform the squaring operation and summing operations are performed with precision resistors. The non-linear characteristics of the diodes and the multiplicity of cross products obtained during the processing produces an output signal with the relatively high noise level. Additionally, these circuits are temperature sensitive and a desired degree of accuracy is difficult to achieve over a wide temperature range.
Multiplication of two signals, x y by triangle averaging is accomplished by adding the triangle wave to the sum of x+y, adding the triangle wave to the difference x-y, rectifying the first sum to retain the positive portion of the wave, rectifying the second sum to retain the negative portion of the wave, individually passing the two rectified sums through lowpass filters and subtracting the sum of the output of the second filter from the output of the first filter to obtain an output voltage that is equal to xy/A, where A is the amplitude of the triangle wave. Since the output is proportional to 1/A, the amplitude of the triangle wave generator must be extremely stable. The lowpass filters provide an integration function and removes a large ripple component which would otherwise appear at the output. This filtering, however, limits the frequency response of the system and introduces phase shifts that are too large for many applications.
In pulse width/pulse height multiplication, the sum of a triangle wave and one of the input signals (e.g., x) is applied to a zero bias comparator, the output of which is a sequence of pulses with a duty cycle determined by the magnitude and polarity of x and a period equal to the period of the triangle wave. This series of pulses controls an electronic switch which is coupled to an amplifier in such a manner that +y is transmitted therethrough when the switch is in the ON state and zero when the switch is in the OFF state. The output signal of the amplifier is coupled to a lowpass filter wherein a waveform is integrated which possesses a duty cycle proportional to x and a magnitude proportional to y resulting in a signal at the output terminal of the filter that is proportional to the product xy. Pulse width/pulse height multiplication generally suffers from the same problems as triangle averaging multiplication, i.e., lowpass filters are required to reduce ripple and thereby lower the frequency response of the multiplier. Accuracy depends strongly upon the linearity, symmetry and sharpness of the triangle wave, the resistors used in the feedback networks of the amplifiers, which must be precisely matched, and the offset voltage of the comparator. The switching time is a critical error factor and must be small compared with the period of the triangle wave. This places a stringent limit on the upper frequency of the triangle wave and thus on the frequency response of the multiplier.
The variable transconductance of silicon junction semiconductors has been utilized in the prior art to achieve analog multiplications. The transconductance of silicon junction semiconductors, however, varies with temperature which causes the multiplier to be temperature sensitive. Additionally, the non-linear characteristics of the junction are utilized in the multiplicative process which, as stated previously, generates a multiplicity of cross products that contributes to the noise level at the output terminal of the multiplier. Thus, variable transconductance multipliers are both temperature sensitive and noisy.